%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU546^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:00 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 33 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1294 ( 382 equ; 0 cnn)
% Maximal formula atoms : 67 ( 39 avg)
% Number of connectives : 677 ( 20 ~; 18 |; 262 &; 97 @)
% ( 6 <=>; 263 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 188 ( 183 usr; 74 con; 0-4 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 68 ( 28 ^; 28 !; 12 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_77,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_78,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_79,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_80,type,
vNOT: $o > $o ).
thf(func_def_81,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_82,type,
vAND: $o > $o > $o ).
thf(func_def_83,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_84,type,
vIMP: $o > $o > $o ).
thf(func_def_85,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_86,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_87,type,
sP0: $i > $i > $o ).
thf(func_def_88,type,
sP1: $i > $o ).
thf(func_def_89,type,
sP2: $i > $i > $o ).
thf(func_def_90,type,
sP3: $i > $i > $o ).
thf(func_def_91,type,
sP4: $o ).
thf(func_def_93,type,
sK6: $i > $i ).
thf(func_def_94,type,
sK7: $i > $i > $i ).
thf(func_def_99,type,
sK12: $i > $o ).
thf(func_def_102,type,
sK15: $i > $o ).
thf(func_def_103,type,
sK16: $i > $i ).
thf(func_def_104,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_107,type,
sK20: $i > $i > $i ).
thf(func_def_111,type,
sK24: $o > $i > $i > $i ).
thf(func_def_114,type,
sK27: $o ).
thf(func_def_121,type,
sK34: $i > $i > $i ).
thf(func_def_125,type,
sK38: $i > $i ).
thf(func_def_126,type,
sK39: $i > $o ).
thf(func_def_128,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_133,type,
sK46: $i > $o ).
thf(func_def_134,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_135,type,
sK48: $i > $o ).
thf(func_def_136,type,
sK49: $i > $i ).
thf(func_def_138,type,
sK51: $o ).
thf(func_def_140,type,
sK53: $i > $i ).
thf(func_def_144,type,
sK57: $o ).
thf(func_def_145,type,
sK58: $i > $o ).
thf(func_def_153,type,
sK66: $i > $i > $i ).
thf(func_def_156,type,
sK69: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK71: $i > $o ).
thf(func_def_160,type,
sK73: $i > $o ).
thf(func_def_167,type,
sK80: $o ).
thf(func_def_171,type,
sK84: $i > $i ).
thf(func_def_174,type,
sK87: ( $i > $o ) > $i > $i ).
thf(func_def_176,type,
sK89: $i > $o ).
thf(func_def_180,type,
sK93: $o ).
thf(func_def_182,type,
sK95: $i > $i ).
thf(func_def_184,type,
sK97: $i > $i ).
thf(func_def_190,type,
sK103: $i > $i > $i ).
thf(func_def_191,type,
sK104: $i > $i > $i ).
thf(func_def_192,type,
sK105: $i > $i > $i ).
thf(func_def_193,type,
sK106: $i > $i > $i ).
thf(func_def_194,type,
sK107: $i > $i > $i > $i ).
thf(func_def_195,type,
sK108: $i > $i ).
thf(func_def_196,type,
sK109: $i > $i ).
thf(func_def_197,type,
sK110: $i > $i ).
thf(func_def_198,type,
sK111: $i > $i ).
thf(func_def_199,type,
sK112: $i > $i > $i > $i ).
thf(func_def_200,type,
sK113: $i > $i > $i > $i ).
thf(func_def_201,type,
sK114: $i > $i > $i ).
thf(func_def_202,type,
sK115: $i > $i > $i ).
thf(func_def_203,type,
sK116: $i > $i > $i ).
thf(func_def_205,type,
sK118: $i > $i ).
thf(func_def_206,type,
sK119: $i > $i ).
thf(func_def_207,type,
sK120: $i > $i ).
thf(func_def_208,type,
sK121: $i > $i > $i ).
thf(func_def_209,type,
sK122: $i > $i > $o ).
thf(func_def_211,type,
sK124: $i > $i ).
thf(func_def_212,type,
sK125: $i > $i ).
thf(func_def_213,type,
sK126: $i > ( $i > $i > $o ) > $i ).
thf(func_def_214,type,
sK127: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_215,type,
sK128: $i > ( $i > $i > $o ) > $i ).
thf(func_def_217,type,
sK130: $i > $i ).
thf(func_def_220,type,
sK133: $i > $o ).
thf(func_def_221,type,
sK134: $i > $o ).
thf(func_def_223,type,
sK136: $i > ( $i > $o ) > $i ).
thf(func_def_224,type,
sK137: $i > $o ).
thf(func_def_227,type,
sK140: $i > $o ).
thf(func_def_229,type,
sK142: ( $i > $o ) > $i ).
thf(func_def_230,type,
sK143: ( $i > $o ) > $i ).
thf(func_def_235,type,
sK148: $i > $o ).
thf(func_def_238,type,
sK151: $i > ( $i > $o ) > $i ).
thf(func_def_240,type,
sK153: $i > $o ).
thf(func_def_246,type,
sK159: $i > $o ).
thf(func_def_248,type,
sK161: ( $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK163: $i > $o ).
thf(func_def_253,type,
sK166: $o ).
thf(func_def_256,type,
sK169: $i > $i > $i ).
thf(func_def_257,type,
sK170: $i > $i > $i ).
thf(func_def_259,type,
sK172: $i > $o ).
thf(func_def_261,type,
sK174: $i > ( $i > $o ) > $i ).
thf(func_def_262,type,
sK175: $i > $o ).
thf(func_def_268,type,
sK181: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK182: $i > $o ).
thf(func_def_270,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_271,type,
sK184: $i > ( $i > $o ) > $i ).
thf(func_def_272,type,
sK185: ( $i > $o ) > $i > $i ).
thf(func_def_273,type,
sK186: ( $i > $o ) > $i ).
thf(func_def_274,type,
sK187: ( $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK188: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK189: ( $i > $o ) > $i ).
thf(func_def_277,type,
sK190: $i > ( $i > $o ) > $i ).
thf(func_def_278,type,
sK191: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_279,type,
sK192: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_280,type,
sK193: ( $i > $o ) > $i ).
thf(func_def_281,type,
sK194: $i > $i ).
thf(func_def_282,type,
sK195: ( $i > $o ) > $i ).
thf(func_def_283,type,
sK196: ( $i > $o ) > $i > $i ).
thf(func_def_284,type,
sK197: ( $i > $o ) > $i ).
thf(func_def_285,type,
sK198: $i > $i ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f65,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X2 = X1 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(f66,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X2 = X1 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
thf(f154,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X2 = X1 ) )
=> ( exu
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f66]) ).
thf(f155,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f188,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
inference(rectify,[],[f1]) ).
thf(f189,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f188]) ).
thf(f251,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) ) )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f155]) ).
thf(f252,plain,
( ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) ) )
& ( emptyI = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( uniqinunit = $true )
& ( setadjoinIR = $true )
& ( notinemptyset = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( emptyInPowerset = $true )
& ( subPowSU = $true )
& ( upairsetIR = $true )
& ( exuE1 = $true )
& ( nonemptyI1 = $true )
& ( notinsingleton = $true )
& ( setunionAx = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( powersetI = $true )
& ( exuE3e = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( prop2set2propI = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan4 = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( powersetE = $true )
& ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( notdallE = $true ) ),
inference(flattening,[],[f251]) ).
thf(f427,plain,
( ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 != X2 ) ) ) )
& ( emptyI = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( uniqinunit = $true )
& ( setadjoinIR = $true )
& ( notinemptyset = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( emptyInPowerset = $true )
& ( subPowSU = $true )
& ( upairsetIR = $true )
& ( exuE1 = $true )
& ( nonemptyI1 = $true )
& ( notinsingleton = $true )
& ( setunionAx = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( powersetI = $true )
& ( exuE3e = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( prop2set2propI = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan4 = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( powersetE = $true )
& ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( notdallE = $true ) ),
inference(nnf_transformation,[],[f252]) ).
thf(f428,plain,
( ( quantDeMorgan3 = $true )
& ( emptysetE = $true )
& ( ( exu
@ ^ [Y0: $i] : ( sK134 @ Y0 ) )
!= $true )
& ! [X2: $i] :
( ( ( sK135 = X2 )
| ( $true
!= ( sK134 @ X2 ) ) )
& ( ( $true
= ( sK134 @ X2 ) )
| ( sK135 != X2 ) ) )
& ( emptyI = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( uniqinunit = $true )
& ( setadjoinIR = $true )
& ( notinemptyset = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( nonemptyE1 = $true )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( notdexE = $true )
& ( noeltsimpempty = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( setext = $true )
& ( upairsetE = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( emptyE1 = $true )
& ( omegaSAx = $true )
& ( prop2setI = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( emptyInPowerset = $true )
& ( subPowSU = $true )
& ( upairsetIR = $true )
& ( exuE1 = $true )
& ( nonemptyI1 = $true )
& ( notinsingleton = $true )
& ( setunionAx = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( powersetI = $true )
& ( exuE3e = $true )
& ( quantDeMorgan2 = $true )
& ( emptyinPowerset = $true )
& ( prop2set2propI = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( wellorderingAx = $true )
& ( quantDeMorgan4 = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( powersetE = $true )
& ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( notdallE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK134,sK135]),skolemize(X0,sK134),skolemize(X1,sK135)],[f427]) ).
thf(f561,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f189]) ).
thf(f745,plain,
! [X2: $i] :
( ( $true
= ( sK134 @ X2 ) )
| ( sK135 != X2 ) ),
inference(cnf_transformation,[],[f428]) ).
thf(f746,plain,
! [X2: $i] :
( ( $true
!= ( sK134 @ X2 ) )
| ( sK135 = X2 ) ),
inference(cnf_transformation,[],[f428]) ).
thf(f747,plain,
( ( exu
@ ^ [Y0: $i] : ( sK134 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f428]) ).
thf(f989,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK134 @ Y0 ) )
!= $true ),
inference(definition_unfolding,[],[f747,f561]) ).
thf(f1065,plain,
( ( sK134 @ sK135 )
= $true ),
inference(equality_resolution,[],[f745]) ).
thf(f1311,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK134 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK134 @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f989]) ).
thf(f1312,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK134 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK134 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1311]) ).
thf(f1313,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK134 @ Y0 )
=> ( X1 = Y0 ) ) )
& ( sK134 @ X1 ) )
= $false ),
inference(beta-eta_normalization,[],[f1312]) ).
thf(f1314,plain,
! [X1: $i] :
( ( ( sK134 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK134 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(and_proxy_clausification,[],[f1313]) ).
thf(f1315,plain,
! [X1: $i] :
( ( ( sK134 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( sK134 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK198 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f1314]) ).
thf(f1316,plain,
! [X1: $i] :
( ( $false
= ( ( sK134 @ ( sK198 @ X1 ) )
=> ( X1
= ( sK198 @ X1 ) ) ) )
| ( ( sK134 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f1315]) ).
thf(f1317,plain,
! [X1: $i] :
( ( ( X1
= ( sK198 @ X1 ) )
= $false )
| ( ( sK134 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1316]) ).
thf(f1318,plain,
! [X1: $i] :
( ( $true
= ( sK134 @ ( sK198 @ X1 ) ) )
| ( ( sK134 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1316]) ).
thf(f1319,plain,
! [X1: $i] :
( ( ( sK198 @ X1 )
!= X1 )
| ( ( sK134 @ X1 )
= $false ) ),
inference(equality_proxy_clausification,[],[f1317]) ).
thf(f1409,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sK198 @ X0 )
= sK135 )
| ( $false
= ( sK134 @ X0 ) ) ),
inference(constrained_superposition,[],[f746,f1318]) ).
thf(f1410,plain,
! [X0: $i] :
( ( ( sK198 @ X0 )
= sK135 )
| ( $false
= ( sK134 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1409]) ).
thf(f1412,plain,
! [X0: $i] :
( ( sK135 != X0 )
| ( $false
= ( sK134 @ X0 ) )
| ( $false
= ( sK134 @ X0 ) ) ),
inference(constrained_superposition,[],[f1319,f1410]) ).
thf(f1414,plain,
! [X0: $i] :
( ( sK135 != X0 )
| ( $false
= ( sK134 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1412]) ).
thf(f1416,plain,
( $false
= ( sK134 @ sK135 ) ),
inference(equality_resolution,[],[f1414]) ).
thf(f1418,plain,
$false = $true,
inference(forward_demodulation,[],[f1416,f1065]) ).
thf(f1419,plain,
$false,
inference(trivial_inequality_removal,[],[f1418]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU546^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n005.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:49:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.30 % (1697371)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (1697376)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3150372598:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (1697377)lrs+10_16_si=on:nwc=1.5:random_seed=2894941114:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (1697378)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3445855560:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (1697378)Instruction limit reached!
% 0.22/0.30 % (1697378)------------------------------
% 0.22/0.30 % (1697378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1697378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1697378)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1697378)Termination reason: Instruction limit
% 0.22/0.30 % (1697378)Termination phase: shuffling
% 0.22/0.30 % (1697378)Time elapsed: 0.003 s
% 0.22/0.30 % (1697378)Peak memory usage: 9 MB
% 0.22/0.30 % (1697378)Instructions burned: 3 (million)
% 0.22/0.30 % (1697376) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1697371-1697376"...
% 0.22/0.30 % (1697376)...printing done.
% 0.22/0.30 % (1697376)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (1697376)------------------------------
% 0.22/0.31 % (1697376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (1697376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (1697376)CaDiCaL version: 2.1.3
% 0.22/0.31 % (1697376)Termination reason: Refutation
% 0.22/0.31 % (1697376)Time elapsed: 0.019 s
% 0.22/0.31 % (1697376)Peak memory usage: 13 MB
% 0.22/0.31 % (1697376)Instructions burned: 70 (million)
% 0.22/0.31 % (1697371)Success in time 0.052 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------